EARTH & SPACE SCIENCE Chapter 27 Planets of the Solar System 27.2 Models of the Solar System

27.2 Models of the Solar System Objectives Compare the models of the universe developed by Ptolemy and Copernicus. Summarize Kepler’s three laws of planetary motion. Describe how Newton explained Kepler’s laws of motion.

Early Models of the Solar System Aristotle suggested a geocentric (Earth-centered) model of the solar system that describes the sun, stars, and other planets revolving around Earth. Aristotle’s model failed to explain retrograde motion where some planets appear to be moving backward in the sky relative to stars. Ptolemy proposed that planets moved in small circles, called epicycles, as they revolved in larger circles around Earth.

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Early Models of the Solar System Copernicus proposed a heliocentric (sun-centered) model of the solar system in which the planets revolved around the sun in the same direction, but at different speeds and distances from the sun. In this model, planets that are slower than Earth appear to move backward. Galileo Galilei observed four moons orbiting Jupiter. on/Physics/NSCI1000/Pseudo- science/Copernicus_vs_Ptolemy.html

Kepler’s Laws Tycho Brahe made many detailed observations of the solar system. After his death, one of his assistants, Johannes Kepler, discovered patterns in Brahe’s observations. The law of ellipses states that each planet orbits the sun in a path called an ellipse – not in a circle (Kepler’s First Law). An ellipse is a closed curve whose shape is determined by two points (foci) within the ellipse.

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Kepler’s Laws In planetary orbits, one focus is located within the sun. Elliptical orbits vary in shape. The eccentricity is determined by dividing the distance between the foci of the ellipse by the length of the major axis. The law of equal areas (Kepler’s second law) states that equal areas are covered in equal amounts of time as an object orbits the sun. This second law addresses the speed at which objects travel at different points in their orbit.

Kepler’s Laws An orbital period is the time required for a body to complete a single orbit. The law of periods (Kepler’s third law) describes the relationship between the average distance of a planet from the sun and the orbital period of the planet. The mathematical equation is K x a 3 = p 2 K is one when the distance is measured in astronomical units and the period is measured in Earth years. Average distance of the planet from the sun is a. The period is noted as p. For example, if astronomers note that Jupiter’s orbital period is 11.9 Earth years, the square of 11.9 is 142 – the cubed number of 5.2 – therefore Jupiter is 5.2 AU from the sun.

Newton’s Explanation of Kepler’s Laws Newton’s explanation of Kepler’s laws can apply to planetary motion as well as objects here on Earth. Inertia is the tendency of an object to resist a change in its motion. An outside force must act on a object to change its motion. Gravity is the force that causes the curvature of the motion of a planet. Gravity is the force of attraction between any two objects in the universe that have mass. The sum of gravitational pull and inertia of motion work together to form the ellipse of a stable orbit.

Newton’s Explanation of Kepler’s Laws The more distant a planet is from the sun, the weaker the pull of gravity between them. The orbits of the outer planets are larger and curved more gently because of the reduced gravitational attraction. The outer planets also have longer periods of revolution than the inner planets.